User:CompactStar/Ordinal interval notation: Difference between revisions

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'''Lefts and rights notation''' ~~(<>)~~ is a notation for [[just intonation]] primarily developed by [[User:CompactStar|CompactStar]]. It represents every just interval as a sequence of lefts/rights and a diatonic degree.

'''Lefts and rights notation''' is a notation for [[just intonation]] primarily developed by [[User:CompactStar|CompactStar]]. It represents every just interval as a sequence of lefts/rights and a diatonic degree.

== Explanation ==

All intervals are given a diatonic degree, derived from their [[7edo]] [[patent val]] mapping. If k is a degree, the central k-th is the simplest (according to [[Tenney height]]) just ratio which is a k-th. For example, the central 3rd is [[5/4]], since it is the simplest 3rd, and the central 7th is [[7/4]], since it is the simplest 7th. The left k-th is the simplest k-th which is flatter than central, and the right k-th is the simplest k-th which is sharper than central. Central ~~is abbreviated as C~~, ~~and~~ left and right are abbreviated as < and > respectively.

All intervals are given a diatonic degree, derived from their [[7edo]] [[patent val]] mapping. If k is a degree, the central k-th is the simplest (according to [[Tenney height]]) just ratio which is a k-th. For example, the central 3rd is [[5/4]], since it is the simplest 3rd, and the central 7th is [[7/4]], since it is the simplest 7th. The left k-th is the simplest k-th which is flatter than central, and the right k-th is the simplest k-th which is sharper than central. Central, left and right are abbreviated as c, l, and r respectively.

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-'''Lefts and rights notation''' (<>) is a notation for [[just intonation]] primarily developed by [[User:CompactStar|CompactStar]]. It represents every just interval as a sequence of lefts/rights and a diatonic degree.
+'''Lefts and rights notation''' is a notation for [[just intonation]] primarily developed by [[User:CompactStar|CompactStar]]. It represents every just interval as a sequence of lefts/rights and a diatonic degree.
 == Explanation ==
-All intervals are given a diatonic degree, derived from their [[7edo]] [[patent val]] mapping. If k is a degree, the central k-th is the simplest (according to [[Tenney height]]) just ratio which is a k-th. For example, the central 3rd is [[5/4]], since it is the simplest 3rd, and the central 7th is [[7/4]], since it is the simplest 7th. The left k-th is the simplest  k-th which is flatter than central, and the right k-th is the simplest k-th which is sharper than central. Central is abbreviated as C, and left and right are abbreviated as < and > respectively.
+All intervals are given a diatonic degree, derived from their [[7edo]] [[patent val]] mapping. If k is a degree, the central k-th is the simplest (according to [[Tenney height]]) just ratio which is a k-th. For example, the central 3rd is [[5/4]], since it is the simplest 3rd, and the central 7th is [[7/4]], since it is the simplest 7th. The left k-th is the simplest  k-th which is flatter than central, and the right k-th is the simplest k-th which is sharper than central. Central, left and right are abbreviated as c, l, and r respectively.